1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
puteri [66]
3 years ago
8

Find the values of x and y that make these triangles congruent by the HL Theorem.

Mathematics
1 answer:
RideAnS [48]3 years ago
7 0

According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.

By using this theorem we can set up the system of equations as follows:

x=y+1 ...(1)

2x+3= 3y + 3 ..(2)

By using equation (1) next step is to plug in y+1 for x in equation (2). So,

2 ( y + 1) + 3 = 3y + 3

2y + 2 + 3 = 3y + 3 By using distribution property.

2y + 5 = 3y + 3

2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.

2y = 3y - 2

2y - 3y = -2 Subtract 3y from each sides.

-y = -2

So, y=2

Next step is to plug in y=2 in equation (1) to get the value of x. Hence,

x= 2+1

=3

So, x=3 and y=2 make these triangles congruent.

So, the correct choice is 3. x = 3, y = 2.

You might be interested in
How many solutions exist for the given equation? 3x(x - 2) = 22 - x
Mila [183]
The solution exist for the given equation are
x=-2
and
x=11/3
5 0
3 years ago
Write the equation of the line that passes through the given points<br> (0,2)) and (-9, -3)
Irina18 [472]

Step-by-step explanation:

Y= m x+ C

m (slope ) = 2 - (_3) / 0 _( - 9 )

= 5 / 9

( O, 2 ) Satisfying equation

2= 5/9 ( 0) + C

C= 2

So eq. is

y= 5/ 9 X + 2

7 0
3 years ago
Which table represents a direct variation function? A table with 6 columns and 2 rows. The first row, x, has the entries, negati
IceJOKER [234]

Answer:

The correct option is;

A table with 6 columns and 2 rows. The first row, x, has entries, negative 3, negative 1, 2, 5, 10. The second row, y, has entries, negative 7.5, negative 2.5, 5.0, 12.5, 25

Please find attached the graphs of the table data

Step-by-step explanation:

Each of the given table data of in the tables are analysed to find direct variation;

Table 1

x,               -3,                 -1,                 2,                5,                10

y,              -4.5,              -3.0,             -1.5,             0.0,              1.5              

-4.5/-3  = 1.5 ≠ -3.0/-1 = 3

No direct variation

Table 2      

x,             -5.5,               -4.5,            -3.5,            -2.5,             -1.5

y,              10,                   8,                 6,              4,                  2

10/(-5.5) = -20/11  ≠ 8/(-4.5) = -16/9

However, 10/(-5.5 + 0.5) = -2 = 8/(-4.5 + 0.5) = -2

Adjusted direct variation

Table 3              

x,              -5.5,               -5.5,             -5.5,           -5.5,            -5.5

y,              -3,                    -1,                 2,                5 ,              10                  

-3/(-5.5) ≠ -1/-5.5

No direct variation

Table 4

x,              -3,                    -1,                2,                  5,             10

y,              -7.5,                 -2.5,            5.0 ,              12.5,         25  

 -7.5/-3 = 2.5 = -2.5/(-1) = 5.0/2 = 12.5/5 =25/10

Direct variation exists        

8 0
3 years ago
Read 2 more answers
Can anyone help me please, I will mark brainliest to the right answer
Blababa [14]

Answer:

y-4=0

Step-by-step explanation:

its the only that doesn't have a x?

3 0
2 years ago
WILL GIVE BRAINLIEST IF ANSWERED NOW
iren [92.7K]

Answer:

y=3x-7

Step-by-step explanation:

lines are parallel hence gradient from the equation in question is the same as the gradient of the equation to be found.. comparing to y=mx+c, eq in question has grad 3... from the formula y-y1=m(x-x1) where (x1,y1) is equal to the point in question

5 0
3 years ago
Other questions:
  • Why is 2 + (−3) equal to −1? (1 point)
    12·2 answers
  • The number 75 can be written as the sum of the squares of 3 different positive integers. what is the sum of these 3 integers?
    9·1 answer
  • Solve for the indicated variable 4c=d for c
    5·1 answer
  • Find the sample size necessary in order to be 95% confident when determining the true mean weight within 2 units (EC2). Assume t
    8·1 answer
  • (Lots of points!) (Dumb answers will be reported!)
    12·2 answers
  • PLEASE HELP
    15·1 answer
  • Ollie says that is 25 is x 1/5 the product is equal to 25 is only correct if not explain why
    9·2 answers
  • the auto parts department of an automotive dealership sends out a mean of 66 special orders daily. what is the probability that,
    5·1 answer
  • I need help with math
    7·1 answer
  • Find m<br> …………….. ………….. …………..
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!